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Numerical simulations suggest that average velocity of a biological cell depends largely on attachment dynamics and less on the forces exerted by the cell. We determine the relationship between two models of cell motion, one based on finite spring constants modeling attachment properties (a randomly switched differential equation) and a limiting case (a centroid model-a generalized random walk) where spring constants are infinite. We prove the main result of this paper, the Expected Velocity Relationship theorem. This result shows that the expected value of the difference between cell locations in the differential equation model at the initial time and at some elapsed time is proportional to the elapsed time. We also show that the relationship is time invariant. Numerical results show the model is consistent with experimental data. [ABSTRACT FROM AUTHOR]